Bring a large pot of water to the boil, then add 1 Tbsp of sea salt and let it dissolve. Add and cook pasta for about 13 minutes, or follow the time indicated on the package directions for al dente. Stir every 2 minutes to make sure it doesn’t stick to the bottom.
Place a large saucepan over medium-low heat and pour in 4–6 tbsp of EVOO. Add the crushed garlic along with a splash of tap water and cook for 30 seconds, just until it turns lightly golden and fragrant.
Add the halved cherry tomatoes and cook for 2–3 minutes, stirring gently as they begin to soften and release their juices. Toss in a few basil leaves with the stalks and mix well. Add a splash of water if needed to keep everything from burning.
Remove the basil leaves and stalks, then transfer the sauce to an immersion blender. Gently pulse for about 20 seconds, just enough to lightly break down the tomatoes while keeping the sauce thick and velvety. Return the blended sauce to the pan over medium-low heat and cook for 1 minute.
Use tongs to transfer pasta straight from the pot into the pan, letting a little of the pasta water fall in with it. Stir to combine, then turn off the heat.
Tear fresh basil leaves by hand and add them to the pan. Add black pepper, grated pecorino, and a splash of pasta water, then mix and toss until the pasta is glossy and evenly coated with the sauce.